@toby-pereira said in Variable house sizes:
Methods that guarantee core stability are of interest to me (see this thread, which I linked to earlier) even if it's not my priority. From what I've read, I think it's still unproven that it's guaranteed that the core is non-empty. But if you use a stability measure (as suggested in the thread) rather than an all-or-nothing, it could be workable regardless.
BTW, we should probably distinguish different-sized cores—the possibility of an empty Hare core is unknown, but Droop cores can definitely be empty (as the Condorcet paradox proves). What I'm interested in is satisfying the Hare core with high probability and satisfying the anti-Droop core guarantee with certainty; i.e. the share of voters who would prefer some other committee is less than 1 / (seats - 1).